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Title: Minimum number of non-zero-entries in a stable matrix exhibiting Turing instability

It is shown that for any positive integer \begin{document}$ n \ge 3 $\end{document}, there is a stable irreducible \begin{document}$ n\times n $\end{document} matrix \begin{document}$ A $\end{document} with \begin{document}$ 2n+1-\lfloor\frac{n}{3}\rfloor $\end{document} nonzero entries exhibiting Turing instability. Moreover, when \begin{document}$ n = 3 $\end{document}, the result is best possible, i.e., every \begin{document}$ 3\times 3 $\end{document} stable matrix with five or fewer nonzero entries will not exhibit Turing instability. Furthermore, we determine all possible \begin{document}$ 3\times 3 $\end{document} irreducible sign pattern matrices with 6 nonzero entries which can be realized by a matrix \begin{document}$ A $\end{document} that exhibits Turing instability.

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Award ID(s):
1853598 1331021
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Discrete and Continuous Dynamical Systems - S
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
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